Rank algorithms for picture processing
Computer Vision, Graphics, and Image Processing
Discrete representation of spatial objects in computer vision
Discrete representation of spatial objects in computer vision
Morphological Erosions and Openings: Fast Algorithms Based on Anchors
Journal of Mathematical Imaging and Vision
Root images of median filters: semi-topological approach
Proceedings of the 11th international conference on Theoretical foundations of computer vision
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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Median filters are frequently used in signal analysis because of their smoothing properties and their insensitivity with respect to outliers in the data. Since median filters are nonlinear filters, the tools of linear theory are not applicable to them. One approach to deal with nonlinear filters consists in investigating their root images (fixed elements or signals transparent to the filter). Whereas for one-dimensional median filters the set of all root signals can be completely characterized, this is not true for higher dimensional filters.In 1989, Döhler stated a result on certain root images for two-dimensional median filters. Although Döhlers results are true for a wide class of median filters, his arguments were not correct and his assertions do not hold universally. In this paper we give a rigorous proof of Döhlers results. Moreover, his approach is generalized to the d-dimensional case.